Frontier Models and Efficiency Measurement

Lab Session 3: Heterogeneity

William Greene

Stern School of Business

New York University

0 Introduction1 Efficiency Measurement2 Frontier Functions3 Stochastic Frontiers4 Production and Cost5 Heterogeneity6 Model Extensions7 Panel Data8 Applications

WHO Data

Heterogeneous Frontier Command

FRONTIER [; COST] ; LHS = the variable

; RHS = ONE, the variables, the additional variables ; EFF = the new variable $

ε(i) = v(i) +/- u(i)

Heterogeneous Frontier Model

FRONTIER ; LHS = LDALE ; RHS = ONE,LHEXP,LHEXP2,LEDUC,

VOICE,GEFF,LPOPDEN,TROPICS

; EFF = UI_WHO $

Heteroscedasticity

ui u i

vi v i

Either or both of

exp[ ]

(heteroscedasticity in inefficiency)

exp[ ]

(heteroscedasticity in random shift)

Variables may be the same or different.

w

w

Effects of Environmental Variable on Efficiency

? Frontier cost function with environmental? Variables, load factor, points served, stage? Length.FRONTIER ; Cost ; Lhs = lc ; Rhs = one,…, loadfctr,log(points),log(stage) $

? How does load factor affect efficiency?SIMULATE ; scenario: & loadfctr = .4(.025).95 ; plot $

Efficiency Estimates|Load Factor

Model Command for Heteroscedasticity

Heterogeneity in the Mean of u(i)

i

i i

2i

i

Mean of u depends on measured variables

u | U |

U ~ N[ , ] (may be heteroscedastic)

= i u

iz

Nonparametric Frontier

Frontier with local

Compute residuals then estimate and given the set of residuals from the nonparametric frontier

Compute efficiencies using residuals and and

Parametric vs. Nonparametric

Latent Class Model